Coupled Effects of Substrate Adhesion and Intermolecular Forces on

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Coupled Effects of Substrate Adhesion and Intermolecular Forces on Polymer Thin Film Glass-Transition Behavior Wenjie Xia† and Sinan Keten*,‡ †

Department of Civil & Environmental Engineering and ‡Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3109, United States S Supporting Information *

ABSTRACT: Intermolecular noncovalent forces between polymer chains influence the mobility and glass-transition temperature (Tg), where weaker interchain interactions, all else being the same, typically results in lower bulk polymer Tg. Using molecular dynamics simulations, here we show that this relation can become invalid for supported ultrathin films when the substrate−polymer interaction is extremely strong and the polymer−polymer interactions are much weaker. This contrasting trend is found to be due to a more pronounced substrate-induced appreciation of the film Tg for polymers with weaker intermolecular interactions and low bulk Tg. We show that optimizing this coupling between substrate adhesion and bulk Tg maximizes thin film Tg, paving the way for tuning film properties through interface nanoengineering.

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INTRODUCTION Decades of research on polymer thin films and nanocomposites have established the importance of understanding material behavior near the interface of organic polymers with inorganic solids. The glass-transition temperature (Tg) is one of the key characteristics that govern the thermomechanics of amorphous polymer thin films. There has been considerable effort, through theory, simulation, and experiment, that has illustrated that the Tg of a polymer shifts from that of bulk measurements when the polymer is deposited as a film of nanoscale thickness. This shift is attributed to the effects of free surface and substrate− polymer interactions.1−6 For free-standing polymer films, the free surfaces are believed to be the main factor resulting in the reduction in Tg by increasing the mobility. For the supported polymer films, the apparent Tg will increase or decrease depending on several factors, most notably the substrate−film interaction strength, film thickness, and free surface effects.1,6−10 For this reason, elucidating ways to tailor material properties via surface engineering has become crucial to improve the performance and durability of photoresists in nanoelectronics,11,12 multifunctional nanocomposites,13 coatings,14,15 and polymeric membranes.16,17 Intermolecular noncovalent interactions between polymer chains can be tailored to tune the Tg of amorphous polymers. In general, without taking the topologies and specific chemical details of polymers into account, stronger intermolecular attraction can induce a higher energy barrier for polymer segments to achieve cooperative segmental mobility and increases the requirement for cooperativity in the dynamics associated with the glass transition, which results in a higher Tg.18,19 For example, the inclusion of polar groups such as © 2013 American Chemical Society

hydroxyl groups can facilitate H-bonds and consequently increase Tg, as seen in polyacrylates.20 Changes in the cooperative dynamics and Tg have also been shown in previous studies of solvent, hydrogen bonding, plasticization and antiplasticization effects on the glass transitions of glass formers.19,21−23 More recent efforts have focused on understanding the coupling between monomer chemical properties and confinement effects in thin films. Overall, thickness-dependent properties of thin films have been attributed to numerous factors such as chain-tacticity-related density variations,15 backbone chain stiffness,24,25 monomer interactions,19 alterations of the repeat units26 as well as retained solvents.27,28 However, the coupled effects of noncovalent intermolecular forces between polymer chains and free surfaces and the confinement effects that arise in thin films remain to be fully explored. This is because it is very challenging to map out the interplay between substrate surface chemistry and polymer chemistry via experiments and atomistic simulations because these parameters cannot be continuously and independently varied. Coarse-grained molecular dynamics (CGMD) simulations based on generic molecular models enable comprehensive studies that aim to elucidate the independent effects of these parameters. Here, we establish a CGMD approach that builds on realistic parameters derived from all-atom MD simulations of PMMA to uncover Tg scaling relationships in thin films with variable polymer−polymer and polymer− Received: July 22, 2013 Revised: September 6, 2013 Published: September 11, 2013 12730

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Figure 1. (a) Mapping from the all-atom to CG model for PMMA, where the CG superatom center is placed at the C1 site. (b) Schematic and snapshots of the supported polymer thin film. nanoelectronics and incidentally exhibit much more pronounced surface and substrate effects. The substrate interaction with the polymer chains is captured by an LJ potential of the form Esub(z) = −4εsp[(σsub/z)12 − (σsub/z)6], where z denotes the distance from the center of the bead to the substrate, εsp is the interfacial energy well depth (varied from 0 to 30 kcal/mol in these studies, where εsp = 0 kcal/mol is a free-standing film), and σsub is the distance at which Esub is zero. The cutoff of the attraction is 15 Å. We elect to use the 12−6 form to keep the same potential terms for intermolecular interaction ε and substrate−film interaction εsp, which allows for easier comparison of the intermolecular forces. Glass-transition calculations are carried out using the method described by Tsige and Taylor32 from the meansquared displacement data of monomers in the chains. Detailed description of the coarse-graining strategy, simulation, and analysis protocols are provided in the Supporting Information.

substrate interaction energies. Most importantly, we test the validity of the hypothesis that supported polymer thin films exhibit a monotonic decrease in their Tg as the intermolecular forces between chains are reduced. This observation is known to hold for bulk polymer materials; however, it is currently unknown whether it can be generalized for supported thin films. Understanding the scaling of thin film Tg with intermolecular energy is crucial to the precise tailoring of thin film mechanical properties that govern the reliability of nanoelectronics, nanocomposites, and stimuli-responsive materials.29 Our investigations are multifold to draw a thorough landscape of the interplay of intermolecular interactions with substrate-induced confinement and free-surface effects. First, scaling with intermolecular we examine bulk polymer Tbulk g energy, ε, which is defined here as the depth of the effective interaction potential energy well between monomers. Second, we investigate free-standing thin films with two free surfaces to quantify the interplay between free-surface effects and intermolecular energy. Third, we examine supported thin films with variable substrate−polymer interaction energies to assess confinement effects, their interplay with free-surface effects, and the coupling of these two competing effects with intermolecular energy (ε).

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RESULTS AND DISCUSSION First, we present an analysis of how the intermolecular interaction strength, ε, governs the Tg of the bulk polymer while keeping other factors such as the polymer backbone rigidity the same. Figure 2 shows this result, where we observe

METHODS

Overview of Molecular Dynamics Simulations. All coarsegrained potential terms are parametrized using the inverse Boltzmann method30,31 from all-atom molecular dynamics simulations of poly(methyl methacrylate) (PMMA), with corrections for noncovalent interactions to match the density and Tg of the bulk polymer (Figure S1). Force and mass centers (i.e., beads) in the CG model, representing one monomer each, are at the central carbon site as shown in Figure 1a. For intermolecular interactions, we employ the Lennard-Jones (LJ) 12−6 potential of the form ULJ(r) = −4ε[(σ/r)12 − (σ/r)6], where ε is the depth of the potential well and σ is the zero point. These two parameters are calibrated to match the density at 300 K as well as the Tg of bulk PMMA. The resultant values of σ and ε are 6.5 Å and 0.3 kcal/mol, respectively, which yield a density of 1.17 g/ cm3 and a bulk Tg of 388.6 K for our CG model. Additionally, the model is validated using experimental data on the Flory−Fox constants for PMMA that define the molecular weight dependence of Tg, which our model readily captures with no additional empirical input (Figure S2). Starting from this basic model, we vary ε from 0.2 to 0.5 kcal/mol to generate polymer models with different intermolecular interaction energies while keeping σ constant for all simulations. It should be noted that once ε is varied it is no longer representative of the original PMMA CG model. CGMD thin film simulations are carried out using 100 chains with 100 monomers each, resulting in an 18-nm-thick thin film (Figure 1b) that is supported on a smooth substrate. We judiciously pick 18 nm as a model film thickness because these ultrathin films in the 5 to 20 nm range have become relevant dimensions for the next generation of

Figure 2. Scaling of the glass-transition temperatures of the bulk as a function of the intermolecular interaction strength ε polymer Tbulk g (from 0.2 to 0.4 kcal/mol) obtained from CG simulations. The dashed line is the modified Flory−Fox best-fit equation.

that increasing ε from 0.2 (more rubbery) to 0.4 kcal/mol (more glassy) leads to an increase in bulk Tg monotonically from about 320 to 410 K in a nonlinear relationship. This is attributed to the greater caging effect that arises from stronger intermolecular interactions that pose a larger energy barrier to cooperative segmental motion.22,33−35 Despite this basic understanding, a simple conceptual relationship between the intermolecular interaction energy and Tg has not been established. Therefore, to describe the trend in bulk Tg versus ε, here we fit the data with a modified Flory−Fox equation of 12731

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the form Tg(ε) = Tg∞(1 − (M/ε)δ), where Tg∞ is the theoretical maximum glass-transition temperature when ε is infinite and M and δ are constants. Our reasoning for using this equation is that similar to molecular weight effects, which the original Flory−Fox equation captures, the effect of the interaction energy between the chains should converge to a maximum value asymptotically; that is, further increases in ε will have a diminishing influence on the free volume and segmental mobility. The obtained values of Tg∞, M ,and δ from our results are 432.1 K, 0.11 kcal/mol, and 2.3, respectively. Next, we aim to answer two key questions pertaining to polymer thin films: (i) How does the free-surface effect on film Tg vary for polymers with low ε (rubbery polymers) compared to those with high ε (glassy polymers)? (ii) How does the interfacial energy between the polymer and the substrate, εsp, influence the film Tg ? A comprehensive analysis of these two effects requires a sweep of two key material parameters, ε and εsp, to uncover their coupled effects on film Tg. To isolate freesurface effects from the substrate effects, we first consider the Tg of the free-standing films by setting εsp = 0. Herein, we bulk define the difference between the film and bulk Tg, Tfilm g − Tg , as ΔTg. Figure 3a illustrates that the magnitude of ΔTg increases with decreasing ε in free-standing films, suggesting a greater depression for rubbery films Tg. (Figure S3 in the Supporting Information shows actual glass-transition curves.) The depression of Tg originates from the free surfaces, which induce a liquidlike layer at a surface and enhance the average mobility of the polymer, as discussed in earlier studies.4,5,7,8,36−39 In polymer thin films, regions near surfaces have a lower density that is often characterized by a region called the interfacial layer. A greater interfacial layer hint thickness in a free-standing film (calculated on the basis of the Gibbs dividing surface (GDS)40 concept, (Figure S4)) is indicative of a larger free-surface effect on mobility and Tfilm g . The results of the thickness of the interfacial layer of free-standing films are listed in Table 1. The calculated hint is larger at T = 450 K (above Tfilm g for all cases) than at T = 250 K (below Tfilm g for all cases). The obtained interfacial thickness is about 0.6 to 1.2 nm, which is in the same range of interfacial thickness values obtained in previous MD simulations for thermoset and thermoplastic thin films.41,42 At both temperatures below and above Tfilm g , the general trend is that the interfacial layer thickness is greater for rubbery polymers, suggesting a greater influence of the free surface for polymers with lower intermolecular interaction strengths. Figure 3b shows the Tg scaling of supported films as a function of the intermolecular interaction strength ε for three different interfacial energy strengths εsp. From our results, a distinct trend emerges for all values of ε. Specifically, the magnitude of ΔTg increases as the attractive interaction strength εsp between the substrate and the film is increased from 1.5 to 30.0 kcal/mol. This observation is consistent with experimental findings and computer simulation results that have shown that the ΔTg is greater for strongly attractive substrates, indicating an appreciation of the film Tg.1,43,44 When we compare the Tg results for the same value of εsp as a function of the intermolecular interaction strength ε, this plot clearly shows that the magnitude of ΔTg decreases with increasing ε, and their relationship is more or less linear within this range. For a weak substrate−film interaction strength εsp = is about 7 K higher than the 1.5 kcal/mol, the measured Tfilm g bulk Tg for the rubbery polymer with ε = 0.2 kcal/mol, which

Figure 3. Values of ΔTg plotted against the intermolecular interaction strength ε (from 0.2 to 0.4 kcal/mol) for (a) a free-standing thin film and (b) a supported thin film with various interfacial energy strengths between the substrate and the polymer. The data is fitted with the dashed slope. The results show that for a rubbery free-standing film the free surface depreciation of Tg is stronger. A similar trend is observed for supported films, but the film−substrate interaction can cause Tg appreciation and change the slope as well. The fitted slopes for εsp = 1.5, 3.0, and 30.0 kcal/mol are −96.8, −145.6, and −198.3 K mol/kcal, respectively.

Table 1. Comparison of Interfacial Thicknesses of FreeStanding Thin Films free-standing thin film (thickness = 18 nm) intermolecular interaction temperature 250 K (below Tfilm g ) 450 K (above Tfilm g )

ε = 0.2 kcal/mol ε = 0.3 kcal/mol 7.0 (±1.5) Å 12.1 (±1.6) Å

6.3 (±0.8) Å 9.2 (±1.5) Å

ε = 0.4 kcal/mol 5.8 (±1.3) Å 8.0 (±0.9) Å

indicates that the substrate−film interfacial effect overwhelms the free surface effect by reducing the chain mobility of the film. However, for the glassy polymer film with ε = 0.4 kcal/mol, the value of Tfilm g is about 10 K below the bulk value, which suggests that the substrate effect is so weak that the free surface effect dominates the Tg of the film. For the intermediate attraction strength (εsp = 3.0 kcal/mol) and the very strong one (εsp = 30.0 kcal/mol), the values of Tfilm are higher than the bulk g value; that is, ΔTg is positive in the range ε = 0.2−0.4 kcal/mol. The maximum predicted ΔTg is on the order of 75 K, which has not been directly observed experimentally because most previous experimental and simulation studies focus on the 12732

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effect of the relative weak substrate−film interaction on the film behaviors, such as H bonds. The magnitude of εsp is usually on the same order of ε. Systematic studies on the confinement behavior arising from the strong substrate−film interactions are yet to be carried out experimentally. However, there have been studies where polymer thin films on strongly attractive surfaces have not exhibited a glass-transition up to 60 K above the bulk glass-transition temperature, as in the case of polystyrene on hydrogen-terminated surfaces.45 Additionally, an appreciation as large as 50 K in the film Tg has been reported from an atomistic simulation study of a 9.5-nm-thick polystyrene film on an implicit attractive wall with a softer (LJ 9−3) potential, where the maximum εsp is 3.0 kcal/mol.43 The largest value of εsp examined in our study is 30.0 kcal/mol. Considering those differences, the predicted change in the film Tg in our study is reasonable because it is the maximum attainable value for the particular system. Further experiments with very large substrate−film interactions, for instance, through the use of complementary electrostatic interactions or photo-cross-linking of side groups on the surface would be needed to validate our results. In conjunction with our previous result of Tg for the freestanding film, which shows that the free surface effect is greater for a rubbery polymer than a glassy one (Figure 3a), the observation in Figure 3b also suggests that the substrate−film interfacial effect is also greater for rubbery polymers, which leads to the appreciation of Tfilm in these cases. Moreover, the g slopes fitted to the data (Figure 3b) become steeper as the value of εsp increases from 1.5 to 30.0 kcal/mol, which suggests that ΔTg decays with ε faster for strong confinement (high εsp) than for weak confinement (low εsp). To understand further the effect of substrate−film interactions on the glass-transition behaviors of the films, the adhesion energy between the film and the substrate is investigated by employing the steered molecular dynamics (SMD) approach based on the theory of Jarzynski’s equality,46−48 which yields estimates for the equilibrium adhesion energy of interfaces. Figure 4b shows several steering MD simulation snapshots during the pulling process. The obtained adhesion energies normalized by the interfacial area from the calculations of the potential of mean force (PMF) (Figure S3) are plotted as a function of ε in Figure 4c for εsp = 1.0 kcal/mol. From this plot, it can be clearly seen that the adhesion energies are greater for a rubbery polymer film than a glassy one. can be scaled with ε (Figure 2), the adhesion Because the Tbulk g energy is plotted as a function of Tgbulk in Figure 4d. Interestingly, we observe an almost linear scaling relationship between Tbulk and the adhesion energy. Because different εsp g values will result in different adhesion energies and film Tg values, whether the linear scaling trend between Tg and the adhesion energies holds for all different εsp values requires more investigation. However, the overall decreasing trend of adhesion energy with increasing ε should hold for different εsp values in our study. On the basis of these observations, we suggest that rubbery films adhere more strongly to the substrate, thereby exhibiting a greater reduction in chain mobility, which leads to a more pronounced substrate effect on Tfilm g . To minimize the free-surface effect, we further assess the Tg scaling of the film under very strong confinement with εsp = 30.0 kcal/mol. This value is large enough that the chains are largely immobilized on the surface by the strong adhesion. Our previous study has shown that the film Tg increases with the

Figure 4. (a) Schematic illustration of a polymer thin film on a substrate subjected to a pulling force. (b) Steered MD simulation snapshots during the pulling process. The beads within the cutoff range of the attraction of the substrate are labeled in yellow. (c) Plot of the adhesion energy as a function of the intermolecular interaction strength ε for the interfacial energy strength (εsp = 1.0 kcal/mol) between the substrate and the film at a temperature of 250 K. The pulling direction is along the z axis, and the pulling rate is 2 m/s. (d) Plot of the adhesion energy against Tbulk g .

substrate−film interaction εsp and approaches an asymptotic value at a very large value of εsp, which is about 20 times larger than the intermolecular interaction strength ε for our CG PMMA model.49 Therefore, we choose to pick up this very high value as the upper limit, which is about 100 times larger than ε and is ensured to be larger than the critical interaction strength, to study the film confinement behaviors. The obtained result 12733

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thin films under such strong confinement can exhibit a peak in Tg while the intermolecular interaction strength diminishes. We emphasize that several other factors also influence Tg in thin films, most notably the molecular weight of the polymers, chain rigidity, and film thickness, which all play a role in the relative importance of the free-surface versus substrate effects. Through these simulations, we solely show the possibility of achieving a peak in film Tg by modifying the intermolecular forces between chains under confinement effects. We speculate that such an effect would most likely be observable experimentally in a polymer thin film that has weak intermolecular interaction energy yet strong adhesion to the surface, for instance, through repulsive intermolecular interactions and complementary surface electrostatic interactions, respectively. The main contribution of our analysis is that the hypothesis that supported polymer thin films exhibit a monotonic decrease in their Tg as the intermolecular forces between chains is reduced does not generally hold for polymer thin films with strong substrate adhesion. Our analysis also generally reveals the greater influence of surface and free surface effects in thin films with weaker intermolecular interactions.

shows that the value of ΔTg decreases linearly with increasing ε. In contrast, the value of Tbulk monotonically increases with g increasing ε. Because of these two distinctly opposite trends, a nonmonotonic scaling relationship between the T gfilm (=Tbulk g +ΔTg) and ε is expected for the film under this strong confinement. Figure 5 shows precisely this effect, where Tfilm is plotted g against the intermolecular interaction strength for the different

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CONCLUSIONS We have performed molecular simulations using an experimentally validated coarse-grain model to analyze the influence of free surface and substrate effects on the glass-transition behavior on model polymer thin films with varying intermolecular interaction energies. The intermolecular interaction plays a crucial role in determining the relative magnitude of the surface effects on polymer Tg, in particular, for ultrathin films, which are becoming more relevant as nanoelectronics tend toward sub-10-nm systems. We show that both the free surface and substrate−film interface have stronger effects on thin film Tg when the constituent material has lower intermolecular interactions and low bulk Tg. For strongly adhesive supporting substrates, the apparent Tg of the films exhibits a peak value as their intermolecular interaction strength decreases, which significantly deviates from their bulk behavior that shows an expected monotonic decrease with reduced intermolecular interactions. Our results show that the surface adhesion and intermolecular forces have coupled effects on film glass-transition phenomena that can be exploited to optimize the film properties via tuning polymer properties as well as surface engineering. Experiments that systematically vary intermolecular interactions are challenging to carry out and make it difficult to directly validate the results presented in this study. However, the observations that surface and substrate effects are more significant in low bulk Tg polymers corroborate earlier experimental findings that looked at the coupling between chain stiffness and surface effects.24,25 Our findings on the coupled effects of surface and polymer interactions pave the way for future experiments and synthesis efforts that may exploit interfacial phenomena in functional nanocomposites and nanomaterials.

Figure 5. Plot of Tfilm vs intermolecular interaction strength ε for g different interfacial energy strengths (εsp = 1.5, 3.0, and 30.0 kcal/mol) between the substrate and the film. The dashed lines are obtained by (Figure 2). adding the fitting functions of ΔTg (Figure 3b) and Tbulk g

substrate−film interactions (εsp = 1.5, 3.0, and 30.0 kcal/mol). bulk Because Tfilm and ΔTg, as a g can be expressed as the sum of Tg comparison, the curves obtained from the fitting results of Tbulk g (Figure 2) and ΔTg (Figure 3b) are plotted together in this figure. For the low substrate−film interaction, Tfilm increases g monotonically with increasing ε. However, interestingly, we observe that the value of Tfilm for εsp = 30.0 kcal/mol only g increases initially with ε for the relatively rubbery polymer at smaller values of ε. This indicates that the increase in the intrinsic bulk Tg behavior with ε overwhelms the reduction in ΔTg caused by the reduced substrate−film interfacial effect. The deviation of the Tfilm g data from the fitting curve for ε = 1.5 and 3.0 kcal/mol may suggest that the linear decay of ΔTg as a function of ε for the weak confinement does not hold as ε becomes very large. This is because both the free surface and substrate effect will diminish and Tfilm g will converge to its bulk value for very large ε. The Tfilm g values are almost the same for different εsp values when ε = 0.5 kcal/mol, which indicates that the substrate effect is almost invariant with εsp. For εsp = 30.0 kcal/mol, as ε increases beyond the range of 0.3 to 0.4 kcal/ mol, the value of Tfilm begins to decrease, in which case the g depression of the interfacial effect becomes dominant over the intrinsic Tg behavior with increasing ε. From the plot, a peak value of Tfilm g at about 440 K for the strong confinement can be observed, where ε is approximately in the range of 0.3 to 0.4 kcal/mol, which is well captured by the fitting curve. Conversely, for weakly interacting substrates, no peak is observed and the scaling is monotonic, similar to bulk polymer properties. Our finding illustrates that the coupling of substrate and intermolecular energy strength, leading to a peak in Tfilm for g strongly adhesive substrates, has not yet been observed experimentally. This finding suggests that nanoscale polymer

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ASSOCIATED CONTENT

S Supporting Information *

Extra figures detailing the coarse-graining procedure, glasstransition temperature calculations, density profile of the film, and potential of mean force calculations. This material is available free of charge via the Internet at http://pubs.acs.org. 12734

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AUTHOR INFORMATION

Corresponding Author

*Tel: 847-491-5282. E-mail: [email protected]. Author Contributions

The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS W.X. and S.K. acknowledge support from the departments of civil & environmental engineering and mechanical engineering at Northwestern University. A supercomputing grant from Quest HPC System at Northwestern University is acknowledged. This research was supported by the University Partnership Initiative between Northwestern University and the Dow Chemical Company.

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dx.doi.org/10.1021/la402800j | Langmuir 2013, 29, 12730−12736